A long horizontal rod has a bead which can slide along its length and is initially placed at a distance L from one end A. the rod is rotated in a horizontal plane about end A, with a constant angular acceleration α = 0.1 rad/s². The coefficient of friction between rod and bead is μ = 0.4. Neglecting gravity, the time after which the bead starts slipping is ________ sec.
Physics · Mixed Chapter
JEE Mains

Question

A long horizontal rod has a bead which can slide along its length and is initially placed at a distance L from one end A. the rod is rotated in a horizontal plane about end A, with a constant angular acceleration α = 0.1 rad/s². The coefficient of friction between rod and bead is μ = 0.4. Neglecting gravity, the time after which the bead starts slipping is ________ sec.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Angular acceleration of the rod is α=0.1 rad s⁻² and ω=αt. The bead at distance r needs radial (centripetal) acceleration ω²r and tangential acceleration αr. Step 2: With a free bead constrained by the rod, the normal reaction supplies the tangential force N=mαr; static friction along the rod supplies radial force f=mω²r. Step 3: Impending slip when f=μN: mω²r=μmαr ⇒ ω²=μα. Step 4: α²t²=μα ⇒t=√(μ/α)=√(0.4/0.1)=2 s. Answer: 2.